### Solve the following equation: $$\frac{2}{(2r - 1)}$$ - $$\frac{5}{3}$$ =  $$\frac{1}{(r + 2)}$$

JAMB 2021

Solve the following equation: $$\frac{2}{(2r - 1)}$$ - $$\frac{5}{3}$$ =  $$\frac{1}{(r + 2)}$$

• A. ( -1,$$\frac{5}{2}$$ )
• B. ( 1, - $$\frac{5}{2}$$ )
• C. ( $$\frac{5}{2}$$, 1 )
• D. (2,1)
##### Explanation

$$\frac{2}{(2r - 1)}$$ - $$\frac{5}{3}$$ =  $$\frac{1}{(r + 2)}$$

$$\frac{2}{(2r - 1)}$$ - $$\frac{1}{(r + 2)}$$  = $$\frac{5}{3}$$

The L.C.M.: (2r - 1) (r + 2)

$$\frac{2(r + 2) - 1(2r - 1)}{(2r - 1) (r + 2)}$$ = $$\frac{5}{3}$$

$$\frac{2r + 4 - 2r + 1}{ (2r - 1) (r + 2)}$$ = $$\frac{5}{3}$$

cross multiply the solution

3 = (2r - 1) (r + 2) or 2r$$^2$$ + 3r - 2 (when expanded)

collect like terms

2r$$^2$$ + 3r - 2 - 3 = 0

2r$$^2$$ + 3r - 5 = 0

Factorize to get x = 1 or - $$\frac{5}{2}$$

There is an explanation video available below.

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